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Is it possible to rotate the Isolines on a Surface Using `MeshFunction`?

What is my problem with MeshFunction?Using Abs in MeshFunction gives incorrect resultsUsing ContourPlot of a Potential surface ImageMeshFunction at azimuthal angles for RegionPlot3DRotate the output of Plot3DSurface MeshFunction with independently spaced parametersRotate the 2D plotRotate polar region with occlusionHow to rotate the curve but not the axes?Tricky use of MeshFunction

5

$begingroup$

This came up in a different context but some expertise in 3D surfaces or the graphic options would be appreciated. I'm trying to extrapolate the curves from any given surface and things seem to be going quite smoothly. All the curves can be grabbed in one more step as a GraphicsComplex. Perfect for more processing. However, now I'm trying to rotate the isolines to get even more control. This is possible in other software but I'm not sure how it was achieved. I assume there is some way to use the MeshFunction to rotate the Mesh through at least 45 degrees but all my searching hasn't brought up anything helpful. A less practical approach might be to find the intersecting curve of a regularly spaced vertical planes.

Plot3D[Cos[(x y)/2], {x, 0, 4}, {y, 0, 8},

BoxRatios->{4,8,1},

Boxed->False,

Axes->False,

ImageSize->Large,

Mesh->{3,8},

PlotStyle->Directive[Lighting->"Neutral",FaceForm[White,Specularity[0.2,10]]]]

plotting graphics

share|improve this question

asked 2 hours ago

BBirdsellBBirdsell

430313

$endgroup$

add a comment | 

5

$begingroup$

This came up in a different context but some expertise in 3D surfaces or the graphic options would be appreciated. I'm trying to extrapolate the curves from any given surface and things seem to be going quite smoothly. All the curves can be grabbed in one more step as a GraphicsComplex. Perfect for more processing. However, now I'm trying to rotate the isolines to get even more control. This is possible in other software but I'm not sure how it was achieved. I assume there is some way to use the MeshFunction to rotate the Mesh through at least 45 degrees but all my searching hasn't brought up anything helpful. A less practical approach might be to find the intersecting curve of a regularly spaced vertical planes.

Plot3D[Cos[(x y)/2], {x, 0, 4}, {y, 0, 8},

BoxRatios->{4,8,1},

Boxed->False,

Axes->False,

ImageSize->Large,

Mesh->{3,8},

PlotStyle->Directive[Lighting->"Neutral",FaceForm[White,Specularity[0.2,10]]]]

plotting graphics

share|improve this question

asked 2 hours ago

BBirdsellBBirdsell

430313

$endgroup$

add a comment | 

$begingroup$

This came up in a different context but some expertise in 3D surfaces or the graphic options would be appreciated. I'm trying to extrapolate the curves from any given surface and things seem to be going quite smoothly. All the curves can be grabbed in one more step as a GraphicsComplex. Perfect for more processing. However, now I'm trying to rotate the isolines to get even more control. This is possible in other software but I'm not sure how it was achieved. I assume there is some way to use the MeshFunction to rotate the Mesh through at least 45 degrees but all my searching hasn't brought up anything helpful. A less practical approach might be to find the intersecting curve of a regularly spaced vertical planes.

Plot3D[Cos[(x y)/2], {x, 0, 4}, {y, 0, 8},

BoxRatios->{4,8,1},

Boxed->False,

Axes->False,

ImageSize->Large,

Mesh->{3,8},

PlotStyle->Directive[Lighting->"Neutral",FaceForm[White,Specularity[0.2,10]]]]

plotting graphics

share|improve this question

asked 2 hours ago

BBirdsellBBirdsell

430313

$endgroup$

Plot3D[Cos[(x y)/2], {x, 0, 4}, {y, 0, 8},

BoxRatios->{4,8,1},

Boxed->False,

Axes->False,

ImageSize->Large,

Mesh->{3,8},

PlotStyle->Directive[Lighting->"Neutral",FaceForm[White,Specularity[0.2,10]]]]

share|improve this question

asked 2 hours ago

BBirdsellBBirdsell

430313

share|improve this question

asked 2 hours ago

BBirdsellBBirdsell

430313

asked 2 hours ago

BBirdsellBBirdsell

430313

asked 2 hours ago

BBirdsellBBirdsell

430313

2 Answers
2

active

oldest

votes

3

$begingroup$

Plot3D[Cos[(x y)/2], {x, 0, 4}, {y, 0, 8}, BoxRatios -> {4, 8, 1}, 

 Boxed -> False, Axes -> False, ImageSize -> Large, 

 MeshFunctions -> {# + #2 &, # - #2 &},

 Mesh -> {3, 8}, 

 PlotStyle -> Directive[Lighting -> "Neutral", FaceForm[White, Specularity[0.2, 10]]]]

share|improve this answer

answered 1 hour ago

kglrkglr

185k10202421

$endgroup$

add a comment | 

0

$begingroup$

Since we have the identity

RotationMatrix[θ] == {AngleVector[-θ], AngleVector[π/2 - θ]}

one can use this to construct a mesh that is arbitrarily oriented; e.g.

With[{θ = π/4}, 

     Plot3D[Cos[x y/2], {x, 0, 4}, {y, 0, 8}, BoxRatios -> Automatic, 

            MeshFunctions -> {AngleVector[-θ].{#, #2} &, 

                              AngleVector[π/2 - θ].{#, #2} &}]]

and you can change the value of θ for other orientations.

share|improve this answer

answered 10 mins ago

J. M. is computer-less♦J. M. is computer-less

96.8k10303462

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  (If anyone is kind enough to edit my post to include the resulting image, please do so.)
  $endgroup$
  – J. M. is computer-less♦
  9 mins ago
  

  
  
  
  

add a comment | 

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3

$begingroup$

Plot3D[Cos[(x y)/2], {x, 0, 4}, {y, 0, 8}, BoxRatios -> {4, 8, 1}, 

 Boxed -> False, Axes -> False, ImageSize -> Large, 

 MeshFunctions -> {# + #2 &, # - #2 &},

 Mesh -> {3, 8}, 

 PlotStyle -> Directive[Lighting -> "Neutral", FaceForm[White, Specularity[0.2, 10]]]]

share|improve this answer

answered 1 hour ago

kglrkglr

185k10202421

$endgroup$

add a comment | 

3

$begingroup$

Plot3D[Cos[(x y)/2], {x, 0, 4}, {y, 0, 8}, BoxRatios -> {4, 8, 1}, 

 Boxed -> False, Axes -> False, ImageSize -> Large, 

 MeshFunctions -> {# + #2 &, # - #2 &},

 Mesh -> {3, 8}, 

 PlotStyle -> Directive[Lighting -> "Neutral", FaceForm[White, Specularity[0.2, 10]]]]

share|improve this answer

answered 1 hour ago

kglrkglr

185k10202421

$endgroup$

add a comment | 

$begingroup$

Plot3D[Cos[(x y)/2], {x, 0, 4}, {y, 0, 8}, BoxRatios -> {4, 8, 1}, 

 Boxed -> False, Axes -> False, ImageSize -> Large, 

 MeshFunctions -> {# + #2 &, # - #2 &},

 Mesh -> {3, 8}, 

 PlotStyle -> Directive[Lighting -> "Neutral", FaceForm[White, Specularity[0.2, 10]]]]

share|improve this answer

answered 1 hour ago

kglrkglr

185k10202421

$endgroup$

Plot3D[Cos[(x y)/2], {x, 0, 4}, {y, 0, 8}, BoxRatios -> {4, 8, 1}, 

 Boxed -> False, Axes -> False, ImageSize -> Large, 

 MeshFunctions -> {# + #2 &, # - #2 &},

 Mesh -> {3, 8}, 

 PlotStyle -> Directive[Lighting -> "Neutral", FaceForm[White, Specularity[0.2, 10]]]]

share|improve this answer

answered 1 hour ago

kglrkglr

185k10202421

answered 1 hour ago

kglrkglr

185k10202421

answered 1 hour ago

kglrkglr

185k10202421

0

$begingroup$

Since we have the identity

RotationMatrix[θ] == {AngleVector[-θ], AngleVector[π/2 - θ]}

one can use this to construct a mesh that is arbitrarily oriented; e.g.

With[{θ = π/4}, 

     Plot3D[Cos[x y/2], {x, 0, 4}, {y, 0, 8}, BoxRatios -> Automatic, 

            MeshFunctions -> {AngleVector[-θ].{#, #2} &, 

                              AngleVector[π/2 - θ].{#, #2} &}]]

and you can change the value of θ for other orientations.

share|improve this answer

answered 10 mins ago

J. M. is computer-less♦J. M. is computer-less

96.8k10303462

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  (If anyone is kind enough to edit my post to include the resulting image, please do so.)
  $endgroup$
  – J. M. is computer-less♦
  9 mins ago
  

  
  
  
  

add a comment | 

0

$begingroup$

Since we have the identity

RotationMatrix[θ] == {AngleVector[-θ], AngleVector[π/2 - θ]}

one can use this to construct a mesh that is arbitrarily oriented; e.g.

With[{θ = π/4}, 

     Plot3D[Cos[x y/2], {x, 0, 4}, {y, 0, 8}, BoxRatios -> Automatic, 

            MeshFunctions -> {AngleVector[-θ].{#, #2} &, 

                              AngleVector[π/2 - θ].{#, #2} &}]]

and you can change the value of θ for other orientations.

share|improve this answer

answered 10 mins ago

J. M. is computer-less♦J. M. is computer-less

96.8k10303462

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  (If anyone is kind enough to edit my post to include the resulting image, please do so.)
  $endgroup$
  – J. M. is computer-less♦
  9 mins ago
  

  
  
  
  

add a comment | 

$begingroup$

Since we have the identity

RotationMatrix[θ] == {AngleVector[-θ], AngleVector[π/2 - θ]}

one can use this to construct a mesh that is arbitrarily oriented; e.g.

With[{θ = π/4}, 

     Plot3D[Cos[x y/2], {x, 0, 4}, {y, 0, 8}, BoxRatios -> Automatic, 

            MeshFunctions -> {AngleVector[-θ].{#, #2} &, 

                              AngleVector[π/2 - θ].{#, #2} &}]]

and you can change the value of θ for other orientations.

share|improve this answer

answered 10 mins ago

J. M. is computer-less♦J. M. is computer-less

96.8k10303462

$endgroup$

RotationMatrix[θ] == {AngleVector[-θ], AngleVector[π/2 - θ]}

With[{θ = π/4}, 

     Plot3D[Cos[x y/2], {x, 0, 4}, {y, 0, 8}, BoxRatios -> Automatic, 

            MeshFunctions -> {AngleVector[-θ].{#, #2} &, 

                              AngleVector[π/2 - θ].{#, #2} &}]]

share|improve this answer

answered 10 mins ago

J. M. is computer-less♦J. M. is computer-less

96.8k10303462

answered 10 mins ago

J. M. is computer-less♦J. M. is computer-less

96.8k10303462

answered 10 mins ago

J. M. is computer-less♦J. M. is computer-less

96.8k10303462